This Exam FM sample reference tests Duration and Convexity. Discounting the three dated amounts at 7% gives a present-value-weighted payment time of 3.314 years, so the keyed answer is choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the discounted cash-flow duration ratio; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the discounted cash-flow duration ratio; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the discounted cash-flow duration ratio; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the discounted cash-flow duration ratio; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: final restoration grant from a target duration
A preservation fund will release 100 at the end of year 1 and an unknown amount K at the end of year 4. At 5% effective annually, its Macaulay duration is exactly 3 years. Determine K.
A 180.00
B 200.00
C 231.53
D 250.00
E 270.00
Variant answer in brief
Solving the duration equation for the later cash flow gives K = 231.53, choice C.
Setup
Setup
The two grants occur at different dates, so their undiscounted amounts are not the duration weights.
v=(1.05)−1
Model
Model
Set the present-value-weighted payment time equal to the required three-year duration.
3=100v+Kv4100v+4Kv4
Compute
Compute
After cross-multiplication, the later grant's present value must be twice the earlier grant's present value.
Kv4=200v,K=200(1.05)3=231.525
Answer
Answer
Accumulating that required present value from year one to year four gives 231.53, choice C.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
